Scatter It! (Using Census Results to
Help Predict Melissa’s Height)
Susan Haller
St. Cloud State University
skhaller@stcloudstate.edu
Published: March 2012
Overview of Lesson
In this lesson, students explore the relationship between age and height in order to help a
hypothetical student predict her height. Students will examine data that will enable them to
create a scatterplot and approximate a line of best fit. The scatterplot and line of best fit will be
used to predict height. The slope of the line of best fit will be interpreted in context.
GAISE Components
This investigation follows the four components of statistical problem solving put forth in the
Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report. The four
components are: formulate a question, design and implement a plan to collect data, analyze the
data by measures and graphs, and interpret the results in the context of the original question.
This is a GAISE Level A activity.
Common Core State Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
Common Core State Standards Grade Level Content (Grade 8)
8. SP. 1. Construct and interpret scatterplots for bivariate measurement data to investigate
patterns of association between two quantities. Describe patterns such as clustering, outliers,
positive or negative association, linear association, and nonlinear association.
8. SP. 2. Know that straight lines are widely used to model relationships between two
quantitative variables. For scatter plots that suggest a linear association, informally fit a straight
line, and informally assess the model fit by judging the closeness of the data points to the line.
8. SP. 3. Use the equation of the linear model to solve problems in the context of bivariate
measurement data, interpreting the slope and intercept.
NCTM Principles and Standards for School Mathematics
Data Analysis and Probability Standards for Grades 6-8
Formulate questions that can be addressed with data and collect, organize, and display
relevant data to answer them:
 formulate questions, design studies, and collect data about a characteristic shared by two
populations or different characteristics within one population;
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
select, create, and use appropriate graphical representations of data, including histograms,
box plots, and scatterplots.
Select and use appropriate statistical methods to analyze data:
 use observations about differences between two or more samples to make conjectures
about the populations from which the samples were taken;
 discuss and understand the correspondence between data sets and their graphical
representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.
Develop and evaluate inferences and predictions that are based on data:
 make conjectures about possible relationships between two characteristics of a sample on
the basis of scatterplots of the data and approximate lines of fit;
 use conjectures to formulate new questions and plan new studies to answer them.
Prerequisites
Students will have knowledge of and experience with graphing points on a coordinate system.
Students will have knowledge of and experience with constructing and evaluating properties of
lines.
Students will have experience using technology to create graphs of data.
Students will have completed Scatter It! (Predict Billy’s Height).
Learning Targets
Students will correctly construct a scatterplot, both manually and with the use of technology.
Students will analyze the scatterplot visually, looking for trends and patterns. In addition,
students will approximate a line of best fit manually, and then create one via technology.
Time Required
One-half class period (assuming students have completed the previous Scatter It! lesson)
Materials Required
 Graphing calculators or computers with software capable of creating scatterplots.
 Spaghetti noodles.
 Graph paper.
 Internet access.
Instructional Lesson Plan
The GAISE Statistical Problem-Solving Procedure
I. Formulate a Question
Begin the lesson by formulating a hypothetical situation:
Melissa is a first-grade student who wants to know how tall she will be when she is in tenthgrade. Her class is studying the census, and Melissa wonders whether information from the
census can help her determine her age when she is in tenth-grade.
Ask students to write some questions that they would be interested in when using the census to
investigate the relationship between age and height. Some possible questions might include:
1. What kinds of information does the census have? Can anyone use this information?
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2. How much information is available on the census? How do we know how much of the
information we should use?
3. Is the relationship between age and height the same for male and female students? If so,
how are they similar? If not, how are they different? Will we know whether the
information comes from a male or female student?
4. Can we use the relationship between age and height from students we don’t know in
order to predict the height of an individual student?
5. Will we get the same results every time we take a sample from the census?
II. Design and Implement a Plan to Collect the Data
Melissa wants to use data from the census to help her predict her age when she is 15.
The table below shows data for 24* randomly selected females from the Census at School web
site: http://www.amstat.org/censusatschool/index.cfm. Students recorded their age in years and
height in centimeters.
Table 1. Age and height for 24 randomly selected female students.
Age
Height
Age
Height
12
153
10
170
11
150
11
144
16
160
16
160
14
166
14
171
12
153
15
171
14
162
14
151
15
164.5
11
154
13
152
10
147
Age
12
13
14
17
12
15
11
11
Height
152.5
156
156
165
156
170.6
157
142
*25 female students were selected, but one student did not have a height recorded, so her data
was eliminated.
When selecting information to be included from the Census web site, note that not all states have
information recorded. You may have to ‘select all’ or select a different state if the state you
wish to sample does not have any data. For the purposes of this exercise, a sample of size 25
works very well. Also, because we wish to forecast the age of a female student, we limit the
gender to female and the age to those from grades 4 – 10.
After selecting the information, delete all columns except the two that pertain to age and height.
Note that some students may have recorded height in inches rather than in centimeters. In this
case you may either choose to convert to cm or eliminate the data.
Use a spreadsheet or graphing calculator to graph the data.
III. Analyze the Data
After the scatterplot of the student data has been constructed, ask students to share anything they
notice within the pattern of growth – does there seem to be a relationship between age and
height? Does this relationship appear to be linear? Discuss the properties of a line of best fit,
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and have students place a piece of spaghetti in their scatterplot to approximate the line of best fit
for the data. Next, have students locate the height of a female at age 15. Students should
compare their results with the rest of the class (predictions will vary because the lines will be
slightly different).
Students should then use the available technology to calculate the line of best fit for the data.
Alternatively, the teacher can calculate it for the students. In this case, the line of best fit is
approximately y = 2.37x + 126.6.
The graph in Figure 1 shows the relationship between age and height for the randomly sampled
female students.
Age/Height Relationship
175
Girls' Heights (in cm)
170
165
160
155
150
145
140
135
6
8
10
12
14
16
18
Girls' Ages
Figure 1. Scatterplot for age and height.
IV. Interpret the Results
The students should next consider the line of best fit in context of the scenario presented.
Students should recognize that the slope indicates that, for the female students in this sample, the
average height increases 2.37 cm for every year of age. Students can then use the equation for
the line of best fit and calculate that the height of the average female student at age 15 should be
between 162 and 163 cm.
Students should also assess the relationship between the graphed data and the line of best fit. For
example, many data points are below the line of best fit, and many above. This means that the
associated heights are below average and above average, respectively.
The teacher should engage the students in a discussion about the constraints for the line of best
fit. For example, the equation would not be appropriate to use with adults.
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Assessment
1. The table below shows the age (in years) and height (in cm) of 24 randomly selected female
students.
Age
15
15
10
14
11
16
Height
152
161
149
163
162
155
Age
Height
15
164
14
175
16
168
15
161
11
153
14
164.5
Age
Height
14
165
14
155
12
157.5
11
148
11
150
12
142.2
Age
Height
12
152.5
11
139
15
161
14
168
10
145
14
163
(a) Construct a graph of the data and describe the relationship between the female students’ age
and height.
(b) Find the equation for the line of best fit for the data.
(c) Predict the height of a randomly selected female at age 17.
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Answers
(a) As age increases, so does height. The relationship appears to be somewhat linear.
Height (cm)
Age/Height Relationship
180
175
170
165
160
155
150
145
140
135
130
8
9
10
11
12
13
14
15
16
17
18
Age (years)
(b) The equation for the line of best fit is y = 2.97x+118.15.
(c) According to the line of best fit, the height should be between 168 and 169 cm.
Possible Extensions
Students can explore the Census at School data to find other variables that may be related. For
example, age and reaction time, or foot length and height. Students might also select data from
two different geographic regions and compare the age/height relationship, or make the same
comparison by segregating by favorite sport.
References
1. This lesson was adapted from an investigation (Scatter It!) found at Census at School – New
Zealand (http://www.censusatschool.org.nz/classroom-activities/).
2. Census data was obtained from Census at School
(http://www.amstat.org/censusatschool/index.cfm).
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Scatter It! Activity Sheet
Melissa is a first-grade student who wants to know how tall she will be when she is in tenthgrade. Her class is studying the census, and Melissa wonders whether information from the
census can help her determine her age when she is in tenth-grade.
1. What are some questions you have about using the census to investigate the relationship
between age and height?
2. The table below shows data for 24 randomly selected females from Census at School
http://www.amstat.org/censusatschool/index.cfm. Students recorded their age in years and
height in centimeters. The original sample included 25 students, but one student was eliminated
because her height was not recorded.
Age
12
11
16
14
12
14
15
13
Height
153
150
160
166
153
162
164.5
152
Age
10
11
16
14
15
14
11
10
Height
170
144
160
171
171
151
154
147
Age
12
13
14
17
12
15
11
13
Height
152.5
156
156
165
156
170.6
157
165
Which variable, age or height, is the independent variable? Why?
3. Use a graphing calculator or computer spreadsheet to construct a graph showing the
relationship between the students’ ages and heights.
4. Describe the relationship you notice about age and height.
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5. Calculate the line of best fit for the data.
What does the slope of the line of best fit mean in this situation?
Use your line of best fit to approximate Melissa’s height when she is 15.
6. Should all classmates get the same equation for the line of best fit for the data above? Why or
why not?
7. Should all classmates get the same equation for the line of best fit if each collected their own
random sample? Why or why not?
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